Question

Direction for question 143 - 145
Read the following information and answer the
questions following it :
Maxine is very fond of collecting greeting cards. She has
a collection of 211 greeting cards with a good mix of birthday
cards, New Year cards, Friendship cards, Christmas cards
and even a marriage anniversary card. The number of birthday
cards is equal to the sum of all the other cards except the
marriage anniversary card. The number of New Year cards is
double of friendship cards which in turn is double of Christmas
cards
b)95
143. The number of birthday cards in the collection is :
a) 105
d)Cannot be determined
c) 115​

Answer 1

Answer:

Option A) 105

Step-by-step explanation:

Let the number of birthday cards be 'b', new year cards be 'n', friendship card be 'f' and Christmas cards be 'c'.

Here we are given she has a marriage anniversary card, which means she has 1 marriage anniversary card.

The number of birthday  cards is equal to the sum of all the other cards except the  marriage anniversary card.

⇒ b = n + f + c

Also, it is given that

n = 2f

f = 2c

⇒ n = 2(2c) = 4c (since, f = 2c)

So, b = n + f + c

⇒ b = 4c + 2c + c

⇒ b = 7c

Now, total number of cards = 211

⇒ b + n + f + c + 1 = 211

(1 is the number of marriage anniversary card)

⇒ b + n + f + c = 210

⇒ 7c + 4c + 2c + c = 210

(since, b = 7c, n = 4c and f = 2c)

⇒ 14c = 210

⇒ c = 210/14

⇒ c = 15

So, number of birthday cards = 7c

⇒ 7 × 15

= 105.

Answer 2

Answer:

105 (Option A)

Step-by-step explanation:

Given Problem:

Maxine is very fond of collecting greeting cards. She has  a collection of 211 greeting cards with a good mix of birthday  cards, New Year cards, Friendship cards, Christmas cards  and even a marriage anniversary card. The number of birthday  cards is equal to the sum of all the other cards except the  marriage anniversary card. The number of New Year cards is  double of friendship cards which in turn is double of Christmas  cards.

b)95

143. The number of birthday cards in the collection is :

a) 105

d)Cannot be determined

c) 115​

Solution:

Let the number of birthday cards be 'a', new year cards be 'm', friendship card be 'p' and Christmas cards be 'x'.

According to your question:

She has a marriage anniversary card, which means she has 1 marriage anniversary card.

The number of birthday cards is equal to the sum of all the other cards not include the marriage anniversary card.

So,

=> a = m + p + x

Given,

m = 2p

p = 2x

Now,

=> m = 2(2x) = 4c (since, p = 2c)

So,

a = m + p + x  

=> a = 4x + 2x + x

=> a = 7x

Now,

Total no. of cards,

= 221

=>a + m + p + x + 1 = 211

★(Here we add 1 number of marriage anniversary card,Because in first steps we didn't add,now we are adding)★

Now,

=>a + m + p+ x = 210

=>7x + 4x + 2x + x = 210

(So, a = 7x, m = 4x and p = 2x)

⇒ 14x = 210  

⇒ x = $\frac{210}{14}$

⇒ x = 15  

Hence,

Number of birthday cards = 7x

⇒ 7 × 15  

★= 105. .........................★(ANSWER)★